GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 16 Dec 2018, 08:11

### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

## Events & Promotions

###### Events & Promotions in December
PrevNext
SuMoTuWeThFrSa
2526272829301
2345678
9101112131415
16171819202122
23242526272829
303112345
Open Detailed Calendar
• ### Free GMAT Prep Hour

December 16, 2018

December 16, 2018

03:00 PM EST

04:00 PM EST

Strategies and techniques for approaching featured GMAT topics
• ### FREE Quant Workshop by e-GMAT!

December 16, 2018

December 16, 2018

07:00 AM PST

09:00 AM PST

Get personalized insights on how to achieve your Target Quant Score.

# Three is the largest number that can be divided evenly into

Author Message
TAGS:

### Hide Tags

Intern
Joined: 11 Feb 2012
Posts: 12
Three is the largest number that can be divided evenly into  [#permalink]

### Show Tags

Updated on: 25 Sep 2012, 00:48
3
26
00:00

Difficulty:

95% (hard)

Question Stats:

46% (02:11) correct 54% (02:18) wrong based on 289 sessions

### HideShow timer Statistics

Three is the largest number that can be divided evenly into 27 and the positive integer x, while 10 is the largest number that can be divided evenly into both 100 and x. Which of the following is the largest possible number that could be divided into x and 2100

A. 30
B. 70
C. 210
D. 300
E. 700

Originally posted by smartass666 on 24 Sep 2012, 19:06.
Last edited by Bunuel on 25 Sep 2012, 00:48, edited 1 time in total.
Renamed the topic and edited the question.
Magoosh GMAT Instructor
Joined: 28 Dec 2011
Posts: 4489

### Show Tags

24 Sep 2012, 20:56
24
3
smartass666 wrote:
Three is the largest number that an be divided evenly into 27 and the positive integer x, while 10 is the largest number that can be divided evenly into both 100 and x. Which of the following is the largest possible number that could be divided into x and 2100
1 - 30
2- 70
3- 210
4 - 300
E - 700

I'm happy to help with this.

This problem has to do with prime factorizations and Greatest Common Factor (GCF). You may find this blog article helpful:
http://magoosh.com/gmat/2012/gmat-math-factors/

27 = 3*3*3, and its GCF with x is 3, which implies that x has ONE factor of 3, but not TWO factors of 3.

100 and x have a GCF of 10, which implies that x has ONE factor of 10, but not TWO factors of 10.

Then we want to know what is the largest possible GCF of x and 2100.

Well 2100 = 3 * 7 * 10 * 10

We want x to include as many factors in common with 2100 as possible, to make the GCF with 2100 as big as possible.

We know x has one factor of 3, but not two factors --- that takes the 3.
We know x has one factor of 10, but not two factors --- we can take one of those 10's, but we have to leave the other
No other restrictions, so we can also grab that factor of 7 --- nothing saying that we can't, and it's there for the taking.

3*7*10 = 210

If we allow x to include as many factors as possible, within the constraints given, that is the most x could have in common with 2100.

Does all that make sense? Please let me know if you have any further questions.

Mike
_________________

Mike McGarry
Magoosh Test Prep

Education is not the filling of a pail, but the lighting of a fire. — William Butler Yeats (1865 – 1939)

Intern
Joined: 20 Sep 2012
Posts: 49
Concentration: Finance, Entrepreneurship
GMAT 1: 750 Q50 V40
GPA: 3.37
WE: Analyst (Consulting)

### Show Tags

24 Sep 2012, 21:00
6
2
Since 3 is the GCF of 27 (3.3.3) and x => x has only one "3 in its prime box.
Since 10 (2.5) is the GCF of 100 (2.2.5.5) and x => x has only one 2 and one 5 in its primebox.
So x = 2.3.5.n (n=something that is not 2, 3, 5)
2100 = 2.3.5.7
The GCF of x and 2100 is the product of the common factors of x and 2100 => the max possible is 2100.
##### General Discussion
Manager
Joined: 04 Feb 2014
Posts: 243
Location: India
Concentration: General Management, Entrepreneurship
GPA: 3
WE: Project Management (Manufacturing)
Three is the largest number that can be divided evenly into 27  [#permalink]

### Show Tags

12 Oct 2015, 16:43
Three is the largest number that can be divided evenly into 27 and the positive integer x, while 10 is the largest number that can be divided evenly into both 100 and x. Which of the following is the largest possible number that could be divided into x and 2100

A. 30
B. 70
C. 210
D. 300
E. 700
_________________

Kudos if you like my post

Manager
Joined: 04 Feb 2014
Posts: 243
Location: India
Concentration: General Management, Entrepreneurship
GPA: 3
WE: Project Management (Manufacturing)
Three is the largest number that can be divided evenly into 27  [#permalink]

### Show Tags

12 Oct 2015, 16:50
Three is the largest number that can be divided evenly into 27 and the positive integer x
So x contains 3

10 is the largest number that can be divided evenly into both 100 and x
So x contains 2 and 5

So x = 2.3.5.n

largest possible number that could be divided into x and 2100
2100= 3*2*2*5*5*7
x = 2.3.5.n

So largest no should be 300=3*5*5*2*2 as it contains 2,3 and 5

What am I doing wrong???
_________________

Kudos if you like my post

EMPOWERgmat Instructor
Status: GMAT Assassin/Co-Founder
Affiliations: EMPOWERgmat
Joined: 19 Dec 2014
Posts: 13095
Location: United States (CA)
GMAT 1: 800 Q51 V49
GRE 1: Q170 V170
Re: Three is the largest number that can be divided evenly into 27  [#permalink]

### Show Tags

12 Oct 2015, 16:56
2
Hi anurag16,

This question can be dealt with in a couple of different ways, but it ultimately comes down to Prime Factorization.

We're told that the largest number that divides into 27 and X is 3.

Since 27 = (3)(3)(3), that means that X's prime factorization can contain JUST ONE 3 (although it can contain other prime factors). If it contained more than one 3, then "3" would NOT be the largest number that would divide into 27 and X.

So X could be 3, 6, 12, 15, 30, etc.

Next, we're told that the largest number that divides into 100 and X is 10.

Since 100 = (2)(2)(5)(5), that means that X's prime factorization can contain JUST ONE 2 AND JUST ONE 5 (although it can contain other prime factors).

So we know that X's prime factorization consists of ONE 2, ONE 3 and ONE 5 and possibly some other primes.

We're asked for the LARGEST number that could divide into X and 2100.

2100 = (3)(7)(2)(2)(5)(5). Using what we know about X, the LARGEST number that could divide X AND 2100 would be (2)(3)(5)(7) = 210.

GMAT assassins aren't born, they're made,
Rich
_________________

760+: Learn What GMAT Assassins Do to Score at the Highest Levels
Contact Rich at: Rich.C@empowergmat.com

# Rich Cohen

Co-Founder & GMAT Assassin

Special Offer: Save \$75 + GMAT Club Tests Free
Official GMAT Exam Packs + 70 Pt. Improvement Guarantee
www.empowergmat.com/

*****Select EMPOWERgmat Courses now include ALL 6 Official GMAC CATs!*****

Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 8678
Location: Pune, India
Re: Three is the largest number that can be divided evenly into  [#permalink]

### Show Tags

12 Oct 2015, 22:12
3
1
smartass666 wrote:
Three is the largest number that can be divided evenly into 27 and the positive integer x, while 10 is the largest number that can be divided evenly into both 100 and x. Which of the following is the largest possible number that could be divided into x and 2100

A. 30
B. 70
C. 210
D. 300
E. 700

This question is based on very simple concepts but the wording is a bit sneaky. We will come to that in a minute.
First, let's quickly analyse what we are given:
3 is the largest number that can be divided evenly into 27 ( = 3^3) and the positive integer x --> 27 has three 3s but only one 3 is common to 27 and x. It means x has exactly one 3.
10 is the largest number that can be divided evenly into both 100 (= 2^2 * 5^2) and x --> Only one 2 and one 5 is common between 100 and x so x has exactly one 2 and exactly one 5.
So x has exactly one 3, one 2 and one 5.

Which of the following is the largest possible number that could be divided into x and 2100?
We need to find the largest possible number that could be divided in x and 2100. Note that x cannot have more than one 3, 2 and 5.
2100 = 2^2 * 3 * 5^2 * 7
It has two 2s and two 5s. But x cannot have two 2s and two 5s - these are two of the limiting conditions we have on x.
What about 7? The questions doesn't tell us whether x has 7. But could it have 7? Sure. We have no limiting condition on having other factors. So the maximum common factors that 2100 and x could have are 2 * 3 * 5 * 7 = 210
So 210 is the largest possible number that could be divided into x and 2100.

_________________

Karishma
Veritas Prep GMAT Instructor

Current Student
Joined: 12 Aug 2015
Posts: 286
Concentration: General Management, Operations
GMAT 1: 640 Q40 V37
GMAT 2: 650 Q43 V36
GMAT 3: 600 Q47 V27
GPA: 3.3
WE: Management Consulting (Consulting)
Three is the largest number that can be divided evenly into  [#permalink]

### Show Tags

21 Mar 2016, 23:22
This question is tricky because of the convoluted language. So x has one 3, one 5 and one 2 as prime factors, and also could have some other primes as no contraints have been set: x = 3*5*2*n. That is 30, 30*7, 30*11, 30*17...

2100 = 7*3*5*2*5*2. These two numbers obviously share such primes as 3*5*2. Since x cannot have more 3s, 2s, and 5s as prime factors we can borrow one 7 from 2100 to construct our max possible common factor of the 2100 and x = 30*7=210.
_________________

KUDO me plenty

Non-Human User
Joined: 09 Sep 2013
Posts: 9184
Re: Three is the largest number that can be divided evenly into  [#permalink]

### Show Tags

05 Jul 2018, 01:18
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________
Re: Three is the largest number that can be divided evenly into &nbs [#permalink] 05 Jul 2018, 01:18
Display posts from previous: Sort by